Publication

An introduction to the synchronization of chaotic systems: coupled skew tent maps

Martin Hasler
1997
Reports

Abstract

In this tutorial paper, various phenomena linked to the synchronization of chaotic systems are discussed using the simple example of two coupled skew tent maps. The phenomenon of locally riddled basins of attraction is explained using the Lyapunov exponents transversal to the synchronization manifold. The skew tent maps are coupled in two different ways, leading to quite different global dynamic behaviors, especially when ideal system is perturbed by parameter mismatch or noise. The linear coupling leads to intermittent desynchronization bursts of large amplitude, whereas for the nonlinear coupling the synchronization error is asymptotically uniformly bounded.

Official source

https://infoscience.epfl.ch/entities/publication/6e1743fb-8bbe-41dc-b961-e577e65fe547

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Martin Hasler
1997
Reports

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6e1743fb-8bbe-41dc-b961-e577e65fe547

About this result

Related concepts (21)

Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.

Chaos theory

Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization.

Nonlinear system

In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.

Related publications (2)

An introduction to the synchronization of chaotic systems: coupled skew tent maps

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